Geometric Sequence Calculator
Find the nth term and the sum of a geometric sequence.
What is Geometric Sequence?
A geometric sequence multiplies by the same amount at every step: 2, 6, 18, 54, … with a common ratio of 3. The nth term is a₁ × r^(n − 1) and the sum of the first n terms is a₁(1 − rⁿ) ÷ (1 − r). It models anything that grows or decays by a percentage — interest, populations, radioactive decay.
How it works
The r = 1 case is handled separately rather than through the sum formula, which divides by 1 − r and would be a division by zero; a constant sequence sums to n copies of a₁ and the page says so. Ratios below 1, zero and negative are all supported, and the sign-alternating and shrinking cases are described in words because the shape of the list is what the ratio controls.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.